Monitor in Power save mode

Hi,
I am having a problem with my computer/monitor and would appreciate very much if I can get some help.

My computer seems to be on all the time and the monitor is in power save mode..so I can see anything on the monitor.
If I shut down the computer manually by pressing the power button and unplug the power cable it comes off...As soon as the power cable is plugged in it starts to boot up on it's own...and the monitor stay in power save mode.

Thanks.